Ljubljanska izjava

Ljubljanska izjava o rabi slovenskega jezika v visokošolskih ustanovah v Sloveniji z namenom ohranjanja jezikovne raznolikosti v Evropski unij

A quadratic lower bound for subset sums

Let A be a finite nonempty subset of an additive abelian group G, and let \Sigma(A) denote the set of all group elements representable as a sum of some subset of A. We prove that |\Sigma(A)| >= |H| + 1/64 |A H|^2 where H is the stabilizer of \Sigma(A). Our result implies that \Sigma(A) = Z/nZ for every set A of units of Z/nZ with |A| >= 8 \sqrt{n}. This consequence was first proved by Erd\H{o}s and Heilbronn for n prime, and by Vu (with a weaker constant) for general n.Comment: 12 page

Is cosmology compatible with sterile neutrinos?

By combining data from cosmic microwave background (CMB) experiments (including the recent WMAP third year results), large scale structure (LSS) and Lyman-alpha forest observations, we constrain the hypothesis of a fourth, sterile, massive neutrino. For the 3 massless + 1 massive neutrino case we bound the mass of the sterile neutrino to m_s<0.26eV (0.44eV) at 95% (99.9%) c.l.. These results exclude at high significance the sterile neutrino hypothesis as an explanation of the LSND anomaly. We then generalize the analysis to account for active neutrino masses (which tightens the limit to m_s<0.23eV 0.42eV) and the possibility that the sterile abundance is not thermal. In the latter case, the contraints in the (mass, density) plane are non-trivial. For a mass of >1eV or <0.05eV the cosmological energy density in sterile neutrinos is always constrained to be omega_nu <0.003 at 95 c.l.. However, for a sterile neutrino mass of ~0.25eV, omega_nu can be as large as 0.01.Comment: 5 pages, 3 figures; v2: update datasets to WMAP3, new Lyman Alpha, Baryonic oscillations; confidence limits tightened by a factor ~2, results unchanged; v3 minor changes, version accepted by PR